Author Topic: Band structure  (Read 4513 times)

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Offline privador

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Band structure
« on: April 15, 2009, 07:28 »
Im intrested in finding band structure for graphenes and nanotubes.
My goal is to get these parametres
1)Fermi level
2)Band gap
3)Brillione zone direction
4)Is it metallic or semiconducting?

Should i choose "method" Brillouin Zone Integration?And can u explain what are these number of k points (A)(B) (C)?
In analysis tab when im intrested calculating energy bands,but i really dont understand what are below tab Band line points(scaled k-points)

About plotting graph.Along the x-axis i see only gamma to K or smth.But how does i know is "gamma" correspond to k=+-pii/a for example.When i resize plot,then there are nothing left in x-axis
I have no idea how to get band gap(Fermi level can be  calculated another analyses tab i presume)
Same problem for determining "metallic or semiconducting" state,because plot seems so crazy and im not sure making right consequences about their state

I looked at ATK tutorial(part 2,page 12) and saw some advanced graph.Is it possible to get the script?



« Last Edit: April 15, 2009, 07:31 by privador »

Offline Anders Blom

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Re: Band structure
« Reply #1 on: April 15, 2009, 09:17 »
First of all, there is a lot of material on the internet and in basic solid state physics text books regarding how to understand the band structure plots, the role and labeling of of k-points, etc, and I think you would need to read them first. It will be hard for us to teach all those basic things via the Forum or a tutorial; we focus on showing how to use the program.

On that note, I am aware of the fact that the band structure functionality in VNL is quite sketchy, and leaves something to be desired. We do however have scripts, that can be used to produce very nice band structure plots like the "advanced" graph you mention, and I will be happy to share them.

It's a bit complex to use, but I will make a tutorial for it, hopefully I can publish it during this week. By that time you have hopefully also studied some more about band structure, and will be ready to use them! :)

A couple of notes to get you started:
  • The value of the Fermi level itself is quite irrelevant. It is really only used as the zero energy reference point for the band structure plot. What matters are how the bands align relative to the Fermi energy, and therefore the Fermi energy is always chosen as zero in the plots.
  • The general rule for choosing k-points in the Kohn-Sham method is, that you need only one k-point in "non-periodic" directions. For a nanotube, this means A (X) and B (Y), if the tube is along C (Z); for a graphene sheet it means C (Z) if they sheet corresponds to the X-Y plane. For a 3D periodic crystal, there is no "non-periodic" direction.
  • The number of k-points also depends on the period length. The longer the period is, the fewer k-points you need. For a small fcc crystal like gold, with a single atom in the unit cell, you probably need 9x9x9 points or so, but if the unit cell is very larger, perhaps 2-3 points are sufficient. For nanotubes I usually use 25-50 points along C to get good accuracy; it's relatively cheap anyway since there is only one point in the A and B directions.
  • ATK is parallelized over k-points, so while increasing the number of k-points makes the calculation take longer time, the effect is less noticeable when you run in parallel.
  • A system is metallic if it has no band gap, i.e. if there are band structure lines crossing the Fermi level. For some peculiar systems, like graphene (infinite 2D sheet), the Fermi "surface" is a single point, which gives this material quite special properties. In general, the most proper way to determine the band gap is to plot the density of states (sorry to bring in another new concept, hope it doesn't confuse you!), but for 1D systems (and often 2D systems) you can often determine the metallic/semiconducting character by just inspecting the band structure.
  • The points Gamma (G) = (0,0,0) and K are high symmetry points in the Brillouin zone where bands cross and there are usually distinct degeneracies. These points serve as "anchor points" for the band structure. It is actually quite difficult to find a good, comprehensive reference on symmetry points for all lattices, since it also matters a bit depending on the exact choice of orientation of the lattice vectors... I will provide some more information in the tutorial.

More to come...!

Offline privador

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Re: Band structure
« Reply #2 on: April 16, 2009, 04:20 »
thx for bothering any answer.i am aware, that DOS is good for band gap .But there arise another problem  with plotting DOS(i cant do it)
Also band structure graphs on the books are "too" beatiful,its easy to determine band gap.
Is it possible to measure band gap somehow?
By the way ,are nanotube grower energy bands  calculated before?And it plots precalculated picture?
The tutorial is great idea and i waiting for it!
« Last Edit: April 16, 2009, 04:37 by privador »

Offline Nordland

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Re: Band structure
« Reply #3 on: April 16, 2009, 07:36 »
I have a small script which you can find here for calculating the band gap.

However it is written for 3D-bulk systems so it needs a small modification to be good suite your system.

Quote
kpoints = [ (i/(2.0*N),j/(2.0*N),k/(2.0*N)) for i in range(-N,N+1) for j in range(-N,N+1) for k in range(0,N+1) ]
needs to be changed to
Quote
kpoints = [ (0,0,k/(2.0*N)) for k in range(0,N+1) ]

And then set N=100 or 200 in the top of the script and you are ready to go!

Offline Anders Blom

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Re: Band structure
« Reply #4 on: April 16, 2009, 08:49 »
For general 3D systems, you can really only determine the band gap from the DOS, since you cannot be sure the minima and maxima lie on the symmetry lines used in the band structure calculation.

The Nanotube Grower uses an analytic tight-binding formula to compute the band structure, that's why it can be done on-the-fly. ;)

Offline hellboy

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Re: Band structure
« Reply #5 on: October 2, 2010, 16:32 »
Dear Sir

Where can i find bandstructure.py script, I am referrin this tutorial http://quantumwise.com/documents/tutorials/Tutorial_Bandstructure.pdf

regards...

Offline Anders Blom

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Re: Band structure
« Reply #6 on: October 2, 2010, 17:03 »
This old script, which has some mistakes for the "difficult lattices" (like body-centered tetragonal etc) can still be obtained from http://quantumwise.com/documents/tutorials/bandstructure.py, for a while still. We're not really supporting ATK 2008.10 anymore, and this functionality it now built into the main ATK code instead.